Hmmm. You don't want to lift if the car is already *oversteering*, but the cure for understeer is to straighten the wheel a bit and lift slightly, which transfers a bit of weight to the front to help regain grip. A touch of left foot brake (if you are so inclined) can help as well. Driving with bald tires in the rain is like driving on ice, everything has to be done very smoothly and gently. Here the "lift and unwind" to deal with understeer is done lightly and progressively. Not that driving with bald tires is ever a good idea, but great practice on a skid pad.
Perhaps what happened here is known in NASCAR parlance as "push-loose". The car initially understeers so you lift to give the front grip. But if you don't unwind the steering wheel at the same time, the front bite now turns the front of the car in the direction of what will become the spin, the rear end is already lightened up from lifting, and you go into snap oversteer.
Of course the cure for oversteer (if the yaw angle and rate are not too severe), is to stay on the gas or even apply a touch more power and countersteer, then wait for the car to hook up and unwind steering so that you do not get secondary oversteer in the opposite direction ("tank slapper"). Using the Skip Barber method that is known as CPR, or "Correct, Pause, Recover."
For Toby's consideration--I have found that lighting up the rear tires in a severe oversteer situation (during the "Pause" portion) reduces friction in the rear and makes for a softer recovery. Then just as the car comes back to straight I lift slightly to let the rear tires slow down and bite, then I hammer the gas and it pulls me straight out. Never have seen this taught, it just came to me at one point after many sideways adventures (all on closed circuit, of course ). Perhaps I picked it up from watching racing--the pros light up the tires in a spin so they don't flatspot the rear. When Joachim Winklehock spins he always seems to end up backing off the track in a reverse direction, so that he does not get hit and can then just hit the gas and go. Very interesting....
--Fred